Ta có:
$4x^2-2y=8+y^2$
$\Leftrightarrow 4x^2-(y+1)^2=7$
$\Leftrightarrow (2x-y-1)(2x+y+1)=7$
$\Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}2x-y-1=1\\2x+y+1=7\end{array}\right.\\\left\{\begin{array}{l}2x-y-1=-1\\2x+y+1=-7\end{array}\right.\\\left\{\begin{array}{l}2x-y-1=7\\2x+y+1=1\end{array}\right.\\\left\{\begin{array}{l}2x-y-1=-7\\2x+y+1=-1\end{array}\right.\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}x=2\\y=2\end{array}\right.\\\left\{\begin{array}{l}x=-2\\y=-4\end{array}\right.\\\left\{\begin{array}{l}x=2\\y=-4\end{array}\right.\\\left\{\begin{array}{l}x=-2\\y=2\end{array}\right.\end{array}\right.$